Lecture 22: Mon, Apr 16. BPP belongs to
P/poly. Same result is unlikely for NP (see below).
Polynomial hierarchy PH. Existence of complete problems for
various levels of PH (all special cases of TQBF). Containment
in PSPACE. Standard assumption: PH does not
"collapse". NP does not belong to P/poly under this
assumption. BPP belongs to the second level of the
hierarchy. Mention Toda's theorem: PH belongs to
P^PP. Problem Set 6 out (on
randomization and interactive protocols, due Wednesday Apr. 25).
Read: Papadimitriou, sec. 11.4, 17.2.